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In the framework of the QCD light-cone sum rules (LCSRs) we present theanalysis of all $B, B_{s}\to \eta^{(\prime)}$ and $D, D_{s}\to \eta^{(\prime)}$form factors ($f^+, f^0$ and $f^T$) by including $m_{\eta^{(\prime)}}^2$corrections in the leading (up to the twist-four) and next-to-leading order (upto the twist-three) in QCD, and two-gluon contributions to the form factors atthe leading twist. The SU(3)-flavour breaking corrections and the axial anomalycontributions to the distribution amplitudes are also consistently taken intoaccount. The complete results for the $f^0$ and $f^T$ form factors of $B,B_s\to \eta^{(\prime)}$ and $D, D_{s} \to \eta^{(\prime)}$ relevant for processeslike $B \to \eta^{(\prime)} \tau \nu_{\tau}$ or $B_{s} \to \eta^{(\prime)} l^+l^-$ are given for the first time, as well as the two-gluon contribution to thetensor form factors. The values obtained for the $f^+$ form factors are asfollows: $f^+_{B\eta}(0)= 0.168^{+0.042}_{-0.047}$, $|f^+_{B_s\eta}(0)|=0.212^{+0.015}_{-0.013}$, $f^+_{B\eta^\prime}(0)= 0.130^{+0.036}_{-0.032}$,$f^+_{B_s\eta^\prime}(0)= 0.252^{+0.023}_{-0.020}$ and $f^+_{D\eta}(0)=0.429^{+0.165}_{-0.141}$, $|f^+_{D_s\eta}(0)|= 0.495^{+0.030}_{-0.029}$,$f^+_{D\eta^\prime}(0)= 0.292^{+0.113}_{-0.104}$, $f^+_{D_s\eta^\prime}(0)=0.558^{+0.047}_{-0.045}$. Also phenomenological predictions for semileptonic$B, B_{s}\to \eta^{(\prime)}$ and $D, D_{s}\to \eta^{(\prime)}$ decay modes aregiven.

Form factors of B, Bs -> eta, eta' and D, Ds -> eta, eta' transitions from QCD light-cone sum rules